Minimum Wage: Unemployment or Higher Prices?

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I was pondering the idea of a $100 minimum wage and had a question. If the minimum wage was $100 wouldn't prices just rise, even though a price floor on a supply and demand curve would claim that workers who currently make over $100 would be the only ones to keep their jobs? Now, I am infering that there would be no underground economy in this scenario where people could work under the table. To me it would seem that people would just raise their prices and keep their employees. If the minimum wage were $100 would there really be no cooks, cashiers, barbers, construction workers, and even most lawyers? So, if these occupations still existed in an economy with a $100 minimum wage and prices just went up, then why wouldn't that happen from a $1 increase?

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If we use the classical definition of inflation, which is an increase in the money supply, then an increase in the minimum wage does not cause inflation. I think you are thinking "rising prices = inflation" but there is a key difference between printing money to raise prices and raising the minimum wage to raise prices. Real purchasing power would plummet if there were a $100 minimum wage, which is not necessarily the case with monetary inflation (theoretically real purchasing power could remain exactly the same). Absent an underground economy, basically everyone would either have to become self-sufficient or die.

Rothard explains the consequences of the triangular intervention that is the state imposing a minimum price on a good - an unsold surplus. For the case of labour this means unemployment. If a firm could charge higher prices for a good, why wouldn't they do so already? Prices are determined by supply and demand not an employer's costs.

... just as the State
has no money of its own, so it has no power of its own - Albert Jay Nock

If the demand curves for the goods made by minimum wage workers/employers looks like this:

Then people will just eat up the price increase and unemployment won't rise. Supply will just shift to the left/upwards and prices will rise to meet this.

Meanwhile if demand curves for the goods in question is perfectly elastic

Then workers will be given the boot exactly until the marginal productivity of their labor is as high as the minimum wage. Since the elasticity of demand for these goods is always somewhere in the middle (probably fairly inelastic)

There are also other very relevant factors: Automation and higher skilled labor. This will affect the elasticity of supply. If the costs of increasing the amount of capital you use, and employing more higher skilled labor you use, then this will decrease the relative value of minimum wage employees, and so as an employer you're much more likely to switch to either of these two options and give your lower skilled workers das boot.

Edit

Also, just as Bogart states, there's also the problem that within any nation there will be competition from other nations without, or with a lower, minimum wage.

At last those coming came and they never looked back
With blinding stars in their eyes but all they saw was black...

This would be the ultimate poor people crushing legislation with or without central bank inflation:

Without central bank inflation the $100 minimum wage would not raise prices but would inhibit production as millions of people would be laid off and domestic production stopped. Now foreign suppliers could still supply goods as they would be able to buy up bankrupted assets in the short term. Keep in mind that without domestic production the tax base would shrink forcing government to either tax imports or cut back on expenditures.

Now with central bank inflation there would be an enormously painful transition period that would completely massacre the finances of the poor as those poor with cash would see the value of that cash decline and those with employment less than 100 would lose their jobs. The employment picture would eventually improve but the transition period would be horrible and the afterwards period would not make up for the losses.

In either case the poor get blasted as they have the lest assets to sell.

So, if there was a $100 minimum wage there would be no barbers, cashiers, etc.?

There still would be if they are profitable above $100/hr. I think some elite NYC/Hollywood hairdressers make more than $100/hr. so there would be a few. Cashiers, not so sure. And remember, we're only talking white-market here. If such a law were passed, doubtless, a great deal of economic activity would go underground into the black-market.

So, if there was a $100 minimum wage there would be no barbers, cashiers, etc.?

There still would be if they are profitable above $100/hr. I think some elite NYC/Hollywood hairdressers make more than $100/hr. so there would be a few. Cashiers, not so sure. And remember, we're only talking white-market here. If such a law were passed, doubtless, a great deal of economic activity would go underground into the black-market.

"There still would be if they are profitable above $100/hr. I think some elite NYC/Hollywood hairdressers make more than $100/hr. so there would be a few. Cashiers, not so sure. And remember, we're only talking white-market here. If such a law were passed, doubtless, a great deal of economic activity would go underground into the black-market."

Remember that even if we ignore the differing qualities of labor there would likely still be employment in various occupations at all but the highest of minimum wages. If there were only 4 people capable of being cashiers in the world, and little to no substitute for cahsiers, then the marginal value of being a cashier would still be that high in some institutions. This is why it's possble for wages to adjust at all with increases in the minimum wagee, because the marginal value of a reduced proportion of labor is higher.

At last those coming came and they never looked back
With blinding stars in their eyes but all they saw was black...